Truth Table, Boolean Expression, K-Map

You have to design an electronic system. In this system you have four on/off switches S1, S2, S3, and S4 as input and two light bulbs (Red and blue) on out put as shown in block diagram below.

This electronic system should work on the following conditions.1. Bulb Red should be ON if switches S1 and S3 are ON2. Bulb Blue should be ON if switches S2 and S4 are ON3. Both the bulbs should remain OFF in any other condition

“You have to first draw the truth table of whole system then after calculating the boolean expression for each bulb, draw the circuit diagram for each bulb”

Your truth table and K-maps look fine. But does the expression S1S3+S2S4 mean? You have two outputs, so you should have two expressions -- one for each output.

While going through the steps explicitlly is worthwhile if you aren't familiar with them yet (and probably required in order to get full credit), the circuitry inside the box should have been obvious to you directly from the specification of the behavior. If it wasn't, be sure to examine the spec in light of your final result until it is.